K. Tanaka


Below are main topics of my research.

Sampling strategy / Discretization of measures with optimization

Sampled values of functions underlie many numerical methods like interpolation and quadrature. To get accurate numerical approximation of functions and their functionals, we need good points for sampling values of the functions. I study methods for obtaining such points in various situation illustrated by the following papers. In particular, I'm interested in methods based on mathematical optimization of quantities evaluating point configurations. They include logarithmic energies, their variants, maximum mean discrepancy, etc.

Representative papers

Study of approximation formulas for holomorphic functions and their integrals

Holomorphic functions are fundamental in scientific computation. I study numerical methods with variable transformations for holomorphic functions. In particular, I focus on methods with Double-Exponential (DE) transformations, which were originally invented by Prof. Takahasi and Prof. Mori for quadrature. Besides quadrature formulas with them, I also study methods approximating functions with sinc funtions and their application. They are collectively called sinc numerical methods. Furthermore, I have proposed improved approximation formulas by minimizing energies with external fields. This study is also related to the above topic about sampling points.

Representative papers

Optimization of variable transformations for approximation formulas

This topic is concerned with the DE variable transformations in the above category. The following papers present methods for improving the variable transformations. In this study, the Schwarz-Christoffel transformations play an important role.

Representative papers

Numerical methods for economics and finance

The following papers are concerned with numerical methods related to economics and finance. In particular, the methods are related to computation of functionals of stochastic processes used in economics and finance. Besides the following papers, there are dissertations of undergraduate and graduate students about this topic.

Representative papers